I have a strip of paper with parallel sides, a pencil and a straight edge.
How can I construct a regular pentagram (star) with these? And for that matter, a pentagon? Well ... the pentagon is the proper way to go.

The solution lies in the trick here. As any veteran paperfolder knows, simply knotting the paper and pressing the knot flat produces a pentagon, and held up to the light the creases inside the figure form a pentagram. use the pencil and straightedge to trace the outlines of the figures. ^^